The Pippen didn't say ''S = the set of all sets''. He said the ''E = set of everything''. I'm paraphrasing a little bit. Do you mean E = S? Why? Afterall the OP is talking about physical stuff (matter and energy) and not about mathematical objects. — TheMadFool

Point certainly taken. I didn't really want to suppress @Pippin's perhaps interesting ideas. It's just that when someone invokes set theory and Russell's paradox, to me that brings in a whole host of baggage. Suppose you do have the empty set {}. Then by the laws of set theory you have its powerset {{}}, and the powerset of that, {{},{{}}}, and the powerset of that, and so forth. You can take a power set for each positive integer; then you can take the union (via another axiom) to get an infinite collection of iterated powersets, and then you can take the powerset of that, and keep on going.

So it's generally a bad idea to call something a "set" if you only mean a collection or perhaps a class. Collections and classes don't have the mathematical baggage that sets do.

But I don't think my criticism was wrong. The OP said the set of "anything (that exists)." That's the literal quote. Then he took its complement, which is an operation on sets, to get the empty set. I'm perfectly within my rights to treat sets as sets.

Perhaps @Pippin can rephrase his ideas without invoking the machinery of set theory.

How do you define nothing?
— Christoffer

Absence of anything. — Marchesk

Doesn't absence make the heart grow fonder? In which case, absence is a thing.

I'm not only using wordplay. Absence is a thing. Suppose you come upon a universe that is empty. You say, "Oranges are absent. Pears are absent. Pomegranates are absent ..." That's a lot of absence, and it takes a mind or an observer to notice it. In a universe containing nothing, there is nothing ... not even absence. This is the same conceptual error the OP is making. Nothing is nothing. There can't be anything. No concepts, not even absence. If you notice there are no oranges, who is doing the noticing?

What does the word absent mean? Something that is supposed to be there, isn't. A student who is supposed to be in class, isn't there that day. She's absent. But a person who isn't enrolled in that class in the first place, is not regarded as being absent from class. You agree? If the class has 30 people enrolled and 29 show up, one is absent. Not seven billion.

I'm not aware of anything in reality that matches that. — Marchesk

But you could perceive the concept that a room is still a room if what is inside it is the absence of anything. From this, the property of nothing as something is what makes the room a room.

Suppose you come upon a universe that is empty. You say, "Oranges are absent. Pears are absent. Pomegranates are absent ..." That's a lot of absence, and it takes a mind or an observer to notice it. In a universe containing nothing, there is nothing ... not even absence. This is the same conceptual error the OP is making. Nothing is nothing. There can't be anything. No concepts, not even absence. If you notice there are no oranges, who is doing the noticing? — fishfry

Exactly. There is no such thing as an entirely empty universe with nothing in it.

You agree? If the class has 30 people enrolled and 29 show up, one is absent. Not seven billion. — fishfry

Agreed. Also all the people that don't exist, or are dead, or will be born.

1. We define (N)othing as the complement of the set of anything (that exists), so N = ∅. — Pippen

Presumably, in order to do this, there are sets.

Presumably, in order to do this, there are sets. — Banno

Sets all the way down.

{{{{{...}}}}}

The infinite set of empty sets?

↪Marchesk {{{{{...}}}}} — Banno

That notation is not supported by the axioms of set theory. It's meaningless unless there are a FINITE number of bracket pairs. You may indeed have {}, {{}}, {{{}}}, ... one term for each positive integer; but to go beyond that you have to take their union. You can not take a limit of this notation.

But I don't think my criticism was wrong. — fishfry

:up: :ok:

again not sure "nothing" is pure abstraction. There are such things as time and space. In a specific space at a specific time there exist either something or nothing. Either option has meaning. — Rank Amateur

Where is nothing in the real world? It's just an idea and can't be physically represented. Space is the best candidate for a physical nothing but it is, if my science is correct, an electromagnetic field. Space isn't nothing.

But I don't think my criticism was wrong. — fishfry

Photons are not conserved. So your proof is experimentally disproved.

Thanks
Bill

1. Let me present you a more simple version of my argument "nothing can come from nothing" which renders a creatio ex nihilo impossible, an argument without sets:

Let's define nothingness as the conjunctions of negations of any possibly or actually existing things: ~p1 & ~p2 & ~p3 & .... From that definition is follows trivially that no object can exist out of nothingness.

2. I still think the set S (representing the Being) of all existing things is neither the set of everything nor does it lead to it. It's different, because it only assumes things that are already existing and therefore non-contradictory, while the set of everything doesn't. Because S exists, ~S exists (~S = empty set = nothingness) and from there it follows trivially as well that if we assume ~S we cannot assume anything out of this empty set.

Yes, this model cannot grasp total nothingness (the same with 1.), but that's how far we can imagine nothingness anyway, there's no consistent way to imagine some more total nothingness because we always need something to define nothingness. Total nothingness is actually meaningless like triangle with four angles, it just looks like it means something due to its letters, but contentwise it's the same as "%$%/&%$/$/$" - meaningless.

Let's define nothingness as the conjunctions of negations of any possibly or actually existing things: ~p1 & ~p2 & ~p3 & .... From that definition is follows trivially that no object can exist out of nothingness. — Pippen

So, dispensing with the unnecessary formalism, what you have stated is that if nothing can possibly exist, then there isn't a possibility of anything existing.

Color me impressed.

If, for the universe or anything to exist, there couldn’t be total ‘nothingness’, what if the ‘something’ that did exist was simply potentiality?
Just a thought - carry on...

1. Let me present you a more simple version of my argument "nothing can come from nothing" which renders a creatio ex nihilo impossible, an argument without sets:

Let's define nothingness as the conjunctions of negations of any possibly or actually existing things: ~p1 & ~p2 & ~p3 & .... From that definition is follows trivially that no object can exist out of nothingness.

2. I still think the set S (representing the Being) of all existing things is neither the set of everything nor does it lead to it. It's different, because it only assumes things that are already existing and therefore non-contradictory, while the set of everything doesn't. Because S exists, ~S exists (~S = empty set = nothingness) and from there it follows trivially as well that if we assume ~S we cannot assume anything out of this empty set.

Yes, this model cannot grasp total nothingness (the same with 1.), but that's how far we can imagine nothingness anyway, there's no consistent way to imagine some more total nothingness because we always need something to define nothingness. Total nothingness is actually meaningless like triangle with four angles, it just looks like it means something due to its letters, but contentwise it's the same as "%$%/&%$/$/$" - meaningless. — Pippen

Aside from the problem of reifying abstractions and positing some questionable definitions there, you don't actually present any sort of argument as to why something can't "come from nothing." You seem to just be assuming that part as obvious, but that's supposed to be what the thread is about. Definitions would only be preliminary work. Once you set out definitions, you need to get on with the argument.

Dudes, the universe does not do what you tell it to. If the universe wants to produce a bowl of petunias from nothing or less than nothing, your arguments are not going to persuade it otherwise. Allow the universe to tell you what what to say, instead of trying to tell it what it must and mustn't do.

Aside from the problem of reifying abstractions and positing some questionable definitions there, you don't actually present any sort of argument as to why something can't "come from nothing." — Terrapin Station

1. Let's postulate only ∅ (Nothingness).
2. Let's assume some t, but that's contradicting 1., so it's impossible.
3. Conclusion: If only ∅ then nothing can exists no matter in which way or modus, nihil ex nihilo.

p.s. It's obvious for me that only ∅ can represent nothingness, one could prove that with raa since any other set would have elements and certainly unable to grasp our intuition of nothing.

p.p.s. Also be aware that Nothingness is relative here since ∅ is not really nothing, but that's our only chance to reason about it; we cannot grasp or refer to absolute nothing since that reference alone would make it something.

p.p.p.s. This proof uses set theory as a model. We could proof the same with just predicate logic by using "There exists nothing" as our assumption, we could even use propositional logic to use "~p1 & ~p2 & ..." to model it roughly.

1. Let's postulate only ∅ (Nothingness).
2. Let's assume some t, but that's contradicting 1., so it's impossible.
3. Conclusion: If only ∅ then nothing can exists no matter in which way or modus, nihil ex nihilo. — Pippen

No one would be saying that there's something and nothing (to the same extent, in the same respect, etc.) at the same time. (2) only contradicts (1) if we assume it's at the same time, to the same extent, etc.

No. If we assume only ∅ then nothing else matters, not even time. No thing can come out of this assumption, no matter how one twists it.

Here is a question that is not often asked in these discussions:

Does nature conform to our ability to comprehend it?

Put differently:

What is logic a reflection of?

We cannot comprehend how something can come from nothing. My claim is that this points to a human limit rather than to some truth about the world.

@fooloso4: We just can reason within our intellectual scope, i.e. logic and meaningful concepts. My proof wants to show that within our scope it's impossible that something can come from nothing. Of course the world could be so different from our reason, our logic could be far off of how the world works, our concepts could be so flawed in comparison to what the world really is all about that we'd be like dogs in a library. We will never conquer that limit but it shouldn't touch us for we can't reason about it anyway, it's just like a big wall we can't look behind. There could be anything, there could be nothing.

No. If we assume only ∅ then nothing else matters, not even time. No thing can come out of this assumption, no matter how one twists it. — Pippen

Again, time matters because that's what people are saying re "something coming from nothing." It's a temporal idea.

You can't successfully argue against a notion if you don't even understand it, or if the argument isn't addressing it but rather a straw man.

@terrapin station:

Ok, let's assume only ∅ + time. Still it's (logically) impossible for a thing to exist from these premises.

I don’t even think there’s an empirical equivalent for nothing. Vacuum space is not empty. Whether there are things like quantum fields or whether they’re just modeling constructs, there’s an intrinsic energetic property to vacuum space which makes it not merely nothing in the philosophical sense. So maybe this argument is equivalent to an argument negating creation from spaghetti soup for all intents and purposes

Here's a better version of my proof of nihil ex nihilo:

1. We postulate the empty set as an universe (= representation of nothingness).
2. We assume some t in the universe which contradicts 1.
3. So it follows that no t can be in the universe.

If you want to add time it's pretty much the same:

1. We postulate the empty set + time as an universe. (= representation of nothingness within time)
2. We assume some t in the universe which contradicts 1.
3. So it follows that no t can be in the universe.

Well if you search for a logical proof, I am not sure there is.

But if we denote by P- something then ~P - nothing.
Then we have the conditional ~P->P which is false if nothing doesn't entail something.

But if nothing existed we could have claimed 'nothing' as something (but that's meta-language mambo jumbo); I think you cannot create something from nothing since it would be like believing that the rabbit wasn't there in the magician's hat to begin with, it just came out of thin air.

I mean all of evolution in biology will be regarded as hogwash if something can come up from nothing, hell all of human evolution started just a few seconds ago ... :-D